| 书目名称 | The Problem of Integrable Discretization | | 副标题 | Hamiltonian Approach | | 编辑 | Yuri B. Suris | | 视频video | | | 概述 | Systematic Hamiltonian recipe of integrable discretization.Unique large collection of results about discrete integrable systems.Unfied treatment of the correspondent continuous integrable systems | | 丛书名称 | Progress in Mathematics | | 图书封面 |  | | 描述 | .The book explores the theory of discrete integrable systems, with an emphasis on the following general problem: how to discretize one or several of independent variables in a given integrable system of differential equations, maintaining the integrability property? This question (related in spirit to such a modern branch of numerical analysis as geometric integration) is treated in the book as an immanent part of the theory of integrable systems, also commonly termed as the theory of solitons.. .Among several possible approaches to this theory, the Hamiltonian one is chosen as the guiding principle. A self-contained exposition of the Hamiltonian (r-matrix, or "Leningrad") approach to integrable systems is given, culminating in the formulation of a general recipe for integrable discretization of r-matrix hierarchies. After that, a detailed systematic study is carried out for the majority of known discrete integrable systems which can be considered as discretizations of integrable ordinary differential or differential-difference (lattice) equations. This study includes, in all cases, a unified treatment of the correspondent continuous integrable systems as well. The list of systems | | 出版日期 | Book 2003 | | 关键词 | Lattice; Matrix; computational and mathematical physics; dynamical systems; numerical analysis | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-0348-8016-9 | | isbn_softcover | 978-3-0348-9404-3 | | isbn_ebook | 978-3-0348-8016-9Series ISSN 0743-1643 Series E-ISSN 2296-505X | | issn_series | 0743-1643 | | copyright | Springer Basel AG 2003 |
The information of publication is updating
|
|
发表于 2025-3-21 18:22:47
